Help Im bad at geometry

In triangle ABC, let the angle bisectors be BY and CZ. Given AB = 16, AY = 16, and CY = 16, find BC and BZ.

Guest Jun 29, 2023

#1**0 **

Let's denote the lengths of BC and BZ as x and y, respectively.

According to the angle bisector theorem, we have:

AY / CY = AB / BC

Substituting the given values, we get:

16 / 16 = 16 / x

Cross-multiplying, we have:

16x = 16 * 16 16x = 256 x = 256 / 16 x = 16

So, BC = 16.

Now, let's consider triangle BCZ. Using the angle bisector theorem again, we have:

BZ / CZ = BC / CY

Substituting the known values, we get:

y / 16 = 16 / 16

Simplifying, we have:

y / 16 = 1

Cross-multiplying, we get:

y = 16

Therefore, BC = 16 and BZ = 16.

Guest Jun 29, 2023